Why can’t matplotlib plot in a different thread?

As other people have told, Matplotlib is not thread safe, one option you have is to use multiprocessing. You say that this is not good for you, because you need access to the axes from different process, but you can overcome this by sharing data between the simulation process and the root process and then managing all the plotting related activities in the root process. For example

import matplotlib
matplotlib.use('TkAgg')
from matplotlib.backends.backend_tkagg import FigureCanvasTkAgg, NavigationToolbar2TkAgg
import multiprocessing
import time
import random
from Tkinter import *


#Create a window
window=Tk()



def main():
    #Create a queue to share data between process
    q = multiprocessing.Queue()

    #Create and start the simulation process
    simulate=multiprocessing.Process(None,simulation,args=(q,))
    simulate.start()

    #Create the base plot
    plot()

    #Call a function to update the plot when there is new data
    updateplot(q)

    window.mainloop()
    print 'Done'


def plot():    #Function to create the base plot, make sure to make global the lines, axes, canvas and any part that you would want to update later

    global line,ax,canvas
    fig = matplotlib.figure.Figure()
    ax = fig.add_subplot(1,1,1)
    canvas = FigureCanvasTkAgg(fig, master=window)
    canvas.show()
    canvas.get_tk_widget().pack(side=TOP, fill=BOTH, expand=1)
    canvas._tkcanvas.pack(side=TOP, fill=BOTH, expand=1)
    line, = ax.plot([1,2,3], [1,2,10])




def updateplot(q):
    try:       #Try to check if there is data in the queue
        result=q.get_nowait()

        if result !='Q':
             print result
                 #here get crazy with the plotting, you have access to all the global variables that you defined in the plot function, and have the data that the simulation sent.
             line.set_ydata([1,result,10])
             ax.draw_artist(line)
             canvas.draw()
             window.after(500,updateplot,q)
        else:
             print 'done'
    except:
        print "empty"
        window.after(500,updateplot,q)


def simulation(q):
    iterations = xrange(100)
    for i in iterations:
        if not i % 10:
            time.sleep(1)
                #here send any data you want to send to the other process, can be any pickable object
            q.put(random.randint(1,10))
    q.put('Q')

if __name__ == '__main__':
    main()